The slope of the line whose equation is x + y = 6 is
a. -1
b. 1
c. 6

Let's rearrange the equation x + y = 6 to slope-intercept form. Solve for y.

x + y = 6

To get the y variable on the left-hand side alone, subtract x from each side.

x + y - x = 6 - x
y = 6 - x

Rearrange the right-hand side.

y = -x + 6

Now we have it in the slope-intercept form. And to find the slope, we look at the coefficient of x. But there is no coefficient of the -x term!

In all reality, there is. However, it's just 1. -1x is the same thing as -x. We don't show the 1 because it has no effect.

So, -1 is the slope.